We present a detailed study of vortex-core spectroscopy in slightly overdoped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ using a low-temperature scanning tunneling microscope. Inside the vortex core, we observe a fourfold symmetric modulation of the local density of states with an energy-independent period of ($4.3\pm 0.3)a_0$. Furthermore, we demonstrate that this square modulation is related to the vortex-core states which are located at $\pm 6\mathrm{meV}$. Since the core-state energy is proportional to the superconducting gap magnitude ${\Delta }_p$, our results strongly suggest the existence of a direct relation between the superconducting state and the local electronic modulations in the vortex core.

• Received 27 December 2004

DOI:https://doi.org/10.1103/PhysRevLett.95.257005